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Factorization of Infinite L-matrices
We present two families of L-matrices and investigate their properties using intricate factorization techniques. These factorization schemes involve...
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Algorithms for Square Root of Semi-Infinite Quasi-Toeplitz M-Matrices
A quasi-Toeplitz M -matrix A is an infinite M -matrix that can be written as the sum of a semi-infinite Toeplitz matrix and a correction matrix. This...
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Isomorphisms of groups of periodic infinite matrices
We study groups of periodic countable matrices that correspond to a Steinitz number (see Bezushchak and Sushchans’kyi in Ukrainian Math J...
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Multiplicative Properties of Infinite Block Toeplitz and Hankel Matrices
We give a simple characterization of when the product of two infinite block Toeplitz matrices is another infinite block Toeplitz matrix. We then use...
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Commutative Matrix Subalgebras Generated by Nonderogatory Matrices
The paper is devoted to the problem of determining the number of subalgebras in the matrix algebra that are generated by nonderogatory matrices and...
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Images of multilinear polynomials on n × n upper triangular matrices over infinite fields
In this paper we prove that the image of multilinear polynomials evaluated on the algebra UT n ( K ) of n × n upper triangular matrices over an infinite...
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Fuzzy Matrices
Like classical (crisp) matrix theory, fuzzy matrix (FM) is also a very useful tool for modelling many uncertain problems that arise in sciences,...
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Deficiency Indices of Block Jacobi Matrices: Survey
The paper is a survey and concerns with infinite symmetric block Jacobi matrices J with m × m -matrix entries. We discuss several results on general...
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Infinite-Dimensional Dynamics
This chapter is dedicated to some generalizations of the notions and results in the former chapters for an infinite-dimensional dynamics. This...
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On the Hankel matrices of finite rank and generalized Fibonacci sequences
In this paper, we propose an approach that utilizes the generalized Fibonacci sequence as a tool for studying the infinite Hankel matrix of finite...
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Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes
This paper presents a survey of recent results on the generalization of distances and divergences on the set of symmetric, positive definite (SPD)...
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Pauli Matrices and Ring Puzzles
We study a family of tessellations of the Euclidean plane which are obtained by local developments of algebraic equations satisfied by the Pauli...
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Positive Semi-Definite Matrices
The present chapter deals essentially with positive semi-definite matrices. It is the longest chapter of the book, but the reader should be aware...
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On some pre-orders and partial orders of linear operators on infinite dimensional vector spaces
This article is devoted to the generalization of the Drazin pre-order and the G-Drazin partial order to Core-Nilpotent endomorphisms over arbitrary k -...
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Twisted Neumann–Zagier matrices
The Neumann–Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra...
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Quantum Permutation Matrices
Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim of this article is to detach these objects from their...
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Universal eigenvalue statistics for dynamically defined matrices
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE...
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On Embeddings of the Free Group into the Group of Infinite Unitriangular Matrices
With the help of the **-pong lemma it is proved that some 2-generated subgroups of the group of infinite unitriangular integer matrices are free....